What is the angle between two vectors if the ratio of their dot product and cross product is√3?​

We cannot divide a quantity by a vector. As cross product of two vectors results in a vector, so ratio of dot product to cross product cannot be obtain. So the question must be written as “ ratio of the magnitudes of the dot product to the cross product”.

Let a and b be two vectors

a.b = abcosθ

|a×b| = absinθ

Given

a.b/|a×b| = √3

=> abcosθ/absinθ = √3

=>cosθ/sinθ  = √3

=> cotθ = √3

=> θ = 30⁰